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If 554b is the base b representation of the square of the number whose base b representation is 24b, then find b.

 May 28, 2018
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\(5b^2+5b+4 = (2b+4)^2\\ 5b^2+5b+4=4b^2+16b+16\\ b^2-11b-12=0\\ (b-12)(b+1)=0\\ b=12 \text{ or } b=-1\text{(rejected)}\\ \therefore b = 12\)

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 May 28, 2018

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